Under his direction, the Office of General Counsel provides legal counsel to the Texas Transportation Commission and the department's administration, districts, divisions, offices and regions. His work includes drafting legislation and administrative rules, testifying before legislative committees and serving as legal counsel at commission meetings.

Before joining TxDOT, Graham served as division chief for the Financial and Taxation Litigation Division, under Texas Attorney General Greg Abbott. Prior to that, he served as the division chief for the Financial Litigation Division of the Office of Attorney General. In 2011, the Taxation Division and Texas Workforce Commission section were added to the office, resulting in the combined Financial and Taxation Litigation Division. In 2012, the Charitable Trust section was also added to his portfolio.

Graham began his career at the Office of the Attorney General in 1997, starting as an administrative technician and moving up to law clerk, then as assistant attorney general and finally division chief.